On real functions. - On infinitely small and infinitely large quantities and on the continuity of functions. Singular values of functions in various particular cases. - On symmetric functions and alternating functions. The use of these functions for the solution of equations of the first degree in any number of unknowns. On homogeneous functions. - Determination of integer functions when a certain number of particular values are known. Applications. - Determination of continuous functions of a single variable that satisfy certain conditions. - On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series. - On imaginary expressions and their moduli. - On imaginary functions and variables. - On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series. - On real or imaginary roots of algebraic equationsfor which the left-hand side is a rational and integer function of one variable. The solution of equations of this kind by algebra or trigonometry. - Decomposition of rational fractions. - On recurrent series. Language: English